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A-LevelMathematicsIntegration9709/21 · May/June 2018 · Q35 Marks

Without using a calculator, find the exact value of ∫₂⁰ 4e⁻ˣ(e³ˣ + 1) dx.

  1. Without using a calculator, find the exact value of ∫₂⁰ 4e⁻ˣ(e³ˣ + 1) dx.[5]

Mark scheme

Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.

  1. [B1] Rewrite integrand as 4e^(2x) + 4e^(-x)
  2. [M1] Integrate to obtain form k₁e^(2x) + k₂e^(-x) where k₁ ≠ 4, k₂ ≠ 4
  3. [A1] Obtain correct 2e^(2x) - 4e^(-x)
  4. [M1] Apply limits correctly, retaining exactness
  5. [A1] Obtain 2e⁴ - 4e⁻² + 2 or exact similarly simplified equivalent

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About this question

Topic
Integration, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, May/June 2018 Paper 2 Variant 1, question 3.

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